The Senate race between GOP Sen. Thad Cochran and his conservative challenger in Mississippi has intensified in advance of a Tuesday primary that is the tea-party movement's last realistic chance this year of ousting a Republican senator.

Mr. Cochran, who is 76 years old and seeking a seventh Senate term, is ending the campaign by trumpeting endorsements from the state's governor and other party power brokers. His challenger, state Sen. Chris McDaniel, is being boosted by appearances with Sarah Palin and other national...